(CBS/AP)-- The House Republican Conference convened on Capitol Hill Saturday to devise a path forward on the budget debate, just one day after the Senate sent them a spending bill that many Republicans view as unacceptable, and just over two days before much of the government will shut down if Congress fails to reach an agreement.

On Friday, the Senate passed a spending bill, called a "continuing resolution," that would keep the government afloat through mid-November and preserve funding for Obamacare, which is scheduled to be almost fully implemented Tuesday.

On Saturday, after the conference meeting, House GOP leaders scheduled a series of votes that would enable their members to volley an amended bill back to the Senate. That bill would fund the government through Dec. 15, but it would also delay Obamacare's requirement for individuals to purchase health insurance by one year and repeal a tax on medical device manufacturers that helps fund the law.

In a statement, House Speaker John Boehner, R-Ohio, along with the rest of the House Republican leadership, described the path forward. "Later today, the House will vote on two amendments to the Senate-passed continuing resolution that will keep the government open and stop as much of the president's health care law as possible," he said. "We will do our job and send this bill over, and then it's up to the Senate to pass it and stop a government shutdown."

The White House reacted to the House Republicans' latest move by putting the blame for a possible shutdown squarely on the GOP's shoulders.

"Any member of the Republican Party who votes for this bill is voting for a shutdown," White House press secretary Jay Carney said in a statement issued late Saturday.

Even if Republicans are able to muscle the bill through the lower chamber, it is unlikely that their latest proposal will pass muster with Senate Democrats and President Obama, who have insisted on a spending bill that keeps the government open without delaying or defunding the healthcare reform law.

"Today's vote by House Republicans is pointless," said Senate Majority Leader Harry Reid, D-Nev., in a statement after the House unveiled its newest proposal. "To be absolutely clear, the Senate will reject both the one-year delay of the Affordable Care Act and the repeal of the medical device tax. After weeks of futile political games from Republicans, we are still at square one: Republicans must decide whether to pass the Senate's clean CR, or force a Republican government shutdown."

"We continue to be willing to debate these issues in a calm and rational atmosphere, but the American people will not be extorted by Tea Party anarchists," he said. The Senate is not scheduled to convene again until Monday.

Mr. Obama has echoed Reid's warning, telling Republicans that their brinksmanship will only serve to hurt the American economy.

"I realize that a lot of what's taking place right now is political grandstanding, but this grandstanding has real effects on real people," he said on Friday after the spending bill cleared the Senate. "Our message to Congress is this: Do not shut down the government. Do not shut down the economy. Pass a budget on time. Pay our bills on time. Refocus on the everyday concerns of the American people... Do not threaten to burn the house down simply because you haven't gotten 100 percent of your way."

On Saturday, in his weekly address, the president twisted the knife further, accusing GOP leaders of kowtowing to their right flank.

"Republicans in the House have been more concerned with appeasing an extreme faction of their party than working to pass a budget that creates new jobs or strengthens the middle class," he said. "And in the next couple days, these Republicans will have to decide whether to join the Senate and keep the government open, or create a crisis that will hurt people for the sole purpose of advancing their ideological agenda."

Indeed, while Republicans in the House have remained largely unified in their desire to defund the health-care law during the budget battle, the fractious debate has exposed some rifts in the Senate GOP caucus.

Conservative hard-liners, led by freshmen Sens. Ted Cruz, R-Texas, and Mike Lee, R-Utah, have pushed their colleagues to insist on a bill that unravels the president's health-care law, but they've been taken to task by some of their more senior colleagues, including Sen. John McCain, R-Ariz., who has said it's not "rational" for Republicans to believe they can scuttle the health-care law during the budget battle.

"This debate has been changed from Republican versus Democrat-slash-Obama to Republican versus Republican, and that cannot be helpful to the Republican Party," McCain said, urging his party to cut their losses and live to fight another day.

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